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Where do numbers come from?





Where do the numbers come from? In "The number devil" Hans Magnus Enzenberger tells us how we can create the numbers 2,3,4,5,6,7, 8 and 9 almost out of nothing. All that is needed is the number 1. See it for yourself. Just multiply 11 * 11 and you get 121. Magically the 2 has appeared. Now multiply 111*111 and you get 12321. Now you got the 3 out of nowhere. Next try 1111*1111. Do you already see a pattern? Yes, the right answer is 1234321. 11111*11111 equals, I think you can guess it now, 123454321. 111111*111111=12345654321 and 1111111*1111111 = 1234567654321 and 11111111*11111111=123456787654321 and finally 111111111*111111111=12345678987654321. Cool, eh?!
Welcome to the fantastic world of numbers!

1*1 = 1
11*11 = 121
111*111 = 12321
1111*1111 = 1234321
11111*11111 = 123454321
111111*111111 = 12345654321
1111111*1111111 = 1234567654321
11111111*11111111 = 123456787654321
111111111*111111111 = 12345678987654321


If you multiply even bigger numbers all composed of 1s the pattern breaks down however as 1111111111*1111111111=1234567900987654321 and 11111111111*11111111111= 123456790120987654321 etc.

You can kind of understand this if you try to multiply these numbers by long multiplication e.g.:

11111 * 11111 =

11111
111110
1111100
11111000
+111110000
----------
123454321
If you multiply with more than 9 1s then you get carry overs and therefore the magic breaks down.

references



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